mathLib

A small, header-only C++17 mathematics library for 2D/3D work: fixed-size vectors, fixed-size matrices, and a simple scene graph. Everything has value semantics and dimensions are encoded in the type, so size mismatches are caught at compile time.

Requirements

• A C++17 compiler (g++, clang++, or MSVC)
• No external dependencies (standard library only)

Components

Header	Provides
vec.h	Vector<T, N> — generic fixed-size vector (base class)
vec2.h	vec2<T> with .x() / .y() accessors and 2D cross
vec3.h	vec3<T> with .x() / .y() / .z() accessors and 3D cross
vec4.h	vec4<T> with .x() / .y() / .z() / .w() accessors
matrix.h	matrix<T, M, N> — fixed-size matrix
SceneGraph.h	SceneNode — hierarchical scene graph
Mesh.h	Minimal Mesh / OGLRenderer stubs used by the scene graph

Vectors

#include "vec3.h"

vec3<float> a(1, 2, 3);
vec3<float> b(4, 5, 6);

auto sum   = a + b;          // component-wise add
auto diff  = a - b;          // component-wise subtract
auto had   = a * b;          // component-wise (Hadamard) product
auto scaled = a * 2.0f;      // scalar multiply (also 2.0f * a)
float d    = a.dot(b);       // dot product
auto c     = a.cross(b);     // cross product (vec3)
float len  = a.length();     // magnitude
auto unit  = a.normalized(); // unit-length copy
float xs   = a.x();          // named accessor
a[0] = 10;                   // indexed access

Also available: operator+= -= *= /=, unary -, operator== / !=, lengthSquared(), and in-place normalize(). vec2::cross returns the scalar signed area (z-component of the 3D cross product).

Matrices

#include "matrix.h"

matrix<float, 2, 3> a;
a(0, 0) = 1.0f;                 // (row, col) access

auto i  = matrix<float, 4, 4>::identity();
auto t  = a.transpose();        // 3x2
auto p  = a * b;                // (2x3)*(3x2) -> 2x2, checked at compile time
auto s  = 2.0f * a;             // scalar multiply
float dt = c.det();             // determinant (square matrices only)

Dimension mismatches (e.g. multiplying incompatible sizes, or taking the determinant of a non-square matrix) are compile-time errors.

Scene graph

#include "SceneGraph.h"

SceneNode root;
SceneNode* child = new SceneNode();   // ownership transfers on AddChild
root.AddChild(child);
root.Update(0.0f);                    // propagates world transforms

A node's world transform is parent.worldTransform * localTransform. Mesh.h provides placeholder Mesh / OGLRenderer types so the scene graph compiles standalone; swap them for your real rendering backend.

Building the demo

g++ -std=c++17 -Wall -Wextra Source.cpp -o mathlib_demo
./mathlib_demo

License

See LICENSE.